Understanding Mathematics through Grappling and Discourse
In Mona Iehl's third grade class at Polaris Charter Academy in Chicago, Illinois, students are developing a conceptual understanding of the commutative property of multiplication. Rather than providing direct instruction, Mona is using a process of grappling and student-centered discourse, which promotes deeper mathematical understanding, and builds powerful habits of learning.
- The 12 groups are the columns because it’s one column, two column, three columns ...
- I think it’s so important that teachers give students time to share and talk about their math thinking. That’s when I’ve seen the deepest thinking from students.
- [Narrator] Mona Iehl’s third graders are developing a conceptual understanding of the commutative property of multiplication. Rather than providing direct instruction Mona is using a process of grappling and student centered discourse which promotes deeper mathematical understanding and builds powerful habits of learning.
- [Mona] I can find all the rectangles with my total tiles. So we always start our class together on the rug focusing on the learning target. Then we always have a time at our seats. We’re working individually to grapple through the content. Each student had a bag of 24 tiles as well as a piece of graph paper with the learning target on it. The goal for students was to build as many different rectangles as they could with all 24 tiles and so in this case students wrote a number model that matched the rectangle that they drew. Its important that kids work independently so that they can grapple through the math content. As I’m walking around I’m also looking for students that I can highlight for the whole crew. That way other students can see how they solved and then hopefully move their understanding even farther. Can you tell the class what you just told me?
- About how those factors switch places when you change the rectangle?
- So now here’s your next challenge. After students have had a sufficient amount of time to explore and grapple with the content for the day and I’ve really been able to find a few examples that I can highlight, I move the students to the rug so that we can have a share and a discourse. We sit in a circle for the share and the discourse so that students can all be accountable to the knowledge that’s being shared. The goal of the discourse is for kids to explain their math thinking, to hear other peoples math thinking and evaluate others mathematical thinking. You’re asking questions and answering your friends questions, you’re sharing your ideas, and you’re using the work to prove your thinking. I noticed that students get to that point of evaluating others math thinking once their able to truly explain their own thinking. So active-listeners on Zack. Tell us how you built this rectangle and what you did to solve to come up with those number models.
- [Zack] I put 12 in each row.
- [Mona] I’m gonna draw it just like Zack drew it on his graph paper and I should see friends all ready getting ideas and thinking. You can be predicting what you think Zack did next.
- I put a line on each two columns.
- So you put a line on these on the columns. What were you thinking about?
- I just did that. I was thinking about putting lines on each two for a whole column and then I thought about switching it and putting a line on each group.
- You turned your rectangle.
- [Zack] Yes
- And you put a line this way. So can groups be columns and rows? Talk with your partner. Can groups be columns and rows? In the discourse its a really great time for students to use their academic vocabulary.
- [Mona] I’m able to notice when students are using certain words and highlight that or have other kids echo it. So you’re saying the columns can be groups but the rows can also be groups? There’s also times where kids don’t have the language for a certain thing and I’m able to just provide the word or the label.
- He did the thing he just did this and this but he didn’t switch it around.
- Okay, so instead of using words like this and that and switch I want to start using math words. Rows and columns or groups, can you use those words to explain how Zack solved this?
- His columns, the reason why he got the answer for his columns because he put the lines and his rows was going like that.
- If I stay true to letting kids think and talk about their thinking I know that they will get there. Look at somebody next to you and say, “You did good thinking today.”
- [Students] You did good thinking today.